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Journal Article

Temporal Variation of the Spectral Decay Parameter Kappa Detected before and after the 2016 Main Earthquakes of Central Italy Available to Purchase

Raúl R. Castro, Daniele Spallarossa, Francesca Pacor, Leonardo Colavitti, Giovanni Lanzano, Claudia A. Vidales‐Basurto, Sara Sgobba
Published: 25 October 2022
Bulletin of the Seismological Society of America (2022) 112 (6): 3037–3045.
DOI: https://doi.org/10.1785/0120220107
...Raúl R. Castro; Daniele Spallarossa; Francesca Pacor; Leonardo Colavitti; Giovanni Lanzano; Claudia A. Vidales‐Basurto; Sara Sgobba ABSTRACT We investigated the temporal variation of the spectral decay parameter κ before and after two main earthquakes that occurred in the central Italy region...
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View PDF for article title, Temporal Variation of the <span class="search-highlight">Spectral</span> <span class="search-highlight">Decay</span> <span class="search-highlight">Parameter</span> Kappa Detected before and after the 2016 Main Earthquakes of Central Italy
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Journal Article

Near‐Source Attenuation and Spatial Variability of the Spectral Decay Parameter Kappa in Central Italy Available to Purchase

Raúl R. Castro, Leonardo Colavitti, Claudia A. Vidales‐Basurto, Francesca Pacor, Sara Sgobba, Giovanni Lanzano
Published: 27 April 2022
Seismological Research Letters (2022) 93 (4): 2299–2310.
DOI: https://doi.org/10.1785/0220210276
...Raúl R. Castro; Leonardo Colavitti; Claudia A. Vidales‐Basurto; Francesca Pacor; Sara Sgobba; Giovanni Lanzano Abstract We study the spectral decay parameter κ using S ‐wave recordings from the central Italy dense regional array. The data set used consists of 266 earthquakes, 353 stations...
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View PDF for article title, Near‐Source Attenuation and Spatial Variability of the <span class="search-highlight">Spectral</span> <span class="search-highlight">Decay</span> <span class="search-highlight">Parameter</span> Kappa in Central Italy
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Journal Article

The Spectral Decay Parameter Kappa in Northeastern Sonora, Mexico Available to Purchase

Avelina I. Fernández, Raúl R. Castro, Carlos I. Huerta
Published: 01 February 2010
Bulletin of the Seismological Society of America (2010) 100 (1): 196–206.
DOI: https://doi.org/10.1785/0120090049
...Avelina I. Fernández; Raúl R. Castro; Carlos I. Huerta Abstract We calculated the spectral decay parameter ( κ ) in the southern Basin and Range province, using records from earthquakes located near the Pitáycachi fault. We found that for a given distance and recording site the values of κ vary...
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View PDF for article title, The <span class="search-highlight">Spectral</span> <span class="search-highlight">Decay</span> <span class="search-highlight">Parameter</span> Kappa in Northeastern Sonora, Mexico
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Journal Article

A preliminary descriptive model for the distance dependence of the spectral decay parameter in southern California Available to Purchase

John G. Anderson
Published: 01 December 1991
Bulletin of the Seismological Society of America (1991) 81 (6): 2186–2193.
DOI: https://doi.org/10.1785/BSSA0810062186
...John G. Anderson Abstract The spectral decay parameter, κ, defined by Anderson and Hough (1984) is described as a function of distance, R , and site, S , as κ( R , S ) = κ 0 ( S ) + κ˜(R). The terms κ˜(R) and κ 0 ( S ) are found by a method that is unbiased by prior assumptions about the nature...
View PDF for article title, A preliminary descriptive model for the distance dependence of the <span class="search-highlight">spectral</span> <span class="search-highlight">decay</span> <span class="search-highlight">parameter</span> in southern California
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Image
An example of the spectral decay parameter in the natural logarithm of normalized amplitude acceleration Fourier amplitude spectra (FAS). (a) Individual normalized acceleration FAS (gray lines) and its average (solid black line). The horizontal‐to‐vertical spectral ratio (HVSR; red dashed line) and a line indicating no site amplification (HVSR = 1; black dotted line) are overlaid. The resonance frequency and its HVSR value are listed in the legend. For each station, frequency limits were manually established to encompass dominant linear attenuation (fm1 and fm2; blue dotted lines). (b) A result of κ estimation for an event. Raw and smoothed spectra are shown as gray and black solid lines, respectively. The initial corner frequency (fc; cyan dotted line) and frequencies of the start and end of the linear slope (fE and fx; gray dotted lines) are shown. The regression result (red dashed line) between fE and fx is plotted. A figure title indicates event ID (including magnitude), network code, station code, and data component. The color version of this figure is available only in the electronic edition.

An example of the spectral decay parameter in the natural logarithm of norm... Available to Purchase

Published: 11 February 2025
Figure 2. An example of the spectral decay parameter in the natural logarithm of normalized amplitude acceleration Fourier amplitude spectra (FAS). (a) Individual normalized acceleration FAS (gray lines) and its average (solid black line). The horizontal‐to‐vertical spectral ratio (HVSR; red
Image
High‐frequency spectral decay parameter kappa (κ) measured from the vertical component of the acceleration spectra of regional event R1. (a) P arrival for κp,acc and (b) S arrival for κs,acc. The spectra are stacked among stations within a subarray of a 2.5 km diameter circle (15–20 stations). The signal spectra (colored) are calculated in a 1.5 s window around the P or S arrivals. The noise spectra (black dotted) are calculated in a 1.5 s window 8 s before the P arrivals. The thin colored lines are linear fits between amplitude (A) and frequency (f) for estimating kappa. We require a minimum frequency bandwidth of 15 Hz. See Figure 2 for the criteria for determining the frequency range. Only one‐fourth of the total spectra and fitting are shown (equally spaced across the array) for visualization. The color version of this figure is available only in the electronic edition.

High‐frequency spectral decay parameter kappa ( κ ) measured from the v... Available to Purchase

Published: 03 January 2025
Figure 3. High‐frequency spectral decay parameter kappa ( κ ) measured from the vertical component of the acceleration spectra of regional event R1. (a)  P arrival for κ p , acc and (b)  S arrival for κ s , a c c . The spectra are stacked among stations within
Image
High‐frequency spectral decay parameter kappa (vertical component): (a) κp,acc and (b) κs,acc, and (c) their comparisons. The kappa values are the median of regional events R1–R3. In panels (a) and (b), each colored circle represents a subarray consisting of stations within a 2.5 km diameter circle (15–20 stations; small, black, hollow circles). The color ranges exclude the 1% lowest and highest values for visualization. The contours indicate the boundaries of the surficial Quaternary formations (Q) versus the Permian formations (P). The error bars in panel (c) are the standard deviation of the fitting. The spectral decay is mostly site‐dependent, with the Quaternary sediments being more attenuating than the Permian rocks. The color version of this figure is available only in the electronic edition.

High‐frequency spectral decay parameter kappa (vertical component): (a)  ... Available to Purchase

Published: 03 January 2025
Figure 4. High‐frequency spectral decay parameter kappa (vertical component): (a)  κ p , acc and (b)  κ s , acc , and (c) their comparisons. The kappa values are the median of regional events R1–R3. In panels (a) and (b), each colored circle represents a subarray consisting
Image
Dependence of spectral decay parameter on epicentral distance (R) for longitudinal and transverse components. The color version of this figure is available only in the electronic edition.

Dependence of spectral decay parameter on epicentral distance ( R ) for lon... Available to Purchase

Published: 01 February 2013
Figure 6. Dependence of spectral decay parameter on epicentral distance ( R ) for longitudinal and transverse components. The color version of this figure is available only in the electronic edition.
Image
Distribution of spectral decay parameters with focal depth for the selected stations, showing the depth dependence of spectral decay parameters at shallow focal depths. The mean and one standard deviation of each distance bin are plotted as squares and vertical lines, respectively. The regression line within 3 km is represented by a red dashed line. The color version of this figure is available only in the electronic edition.

Distribution of spectral decay parameters with focal depth for the selected... Available to Purchase

Published: 11 February 2025
Figure 13. Distribution of spectral decay parameters with focal depth for the selected stations, showing the depth dependence of spectral decay parameters at shallow focal depths. The mean and one standard deviation of each distance bin are plotted as squares and vertical lines, respectively
Image
Distribution of spectral decay parameters (black dots) as a function of (a) epicentral distance, (c) magnitude, and (e) depth. The mean and one standard deviation within each distance bin are plotted as squares and vertical lines, respectively. (b, d, and f) Heatmaps corresponding to panels (a), (c), and (e). The color version of this figure is available only in the electronic edition.

Distribution of spectral decay parameters (black dots) as a function of (a)... Available to Purchase

Published: 11 February 2025
Figure 3. Distribution of spectral decay parameters (black dots) as a function of (a) epicentral distance, (c) magnitude, and (e) depth. The mean and one standard deviation within each distance bin are plotted as squares and vertical lines, respectively. (b, d, and f) Heatmaps corresponding
Image
The relationships between κ‐values, magnitudes, and variables related to frequency windows. The red dashed lines in each figure represent the regression lines corresponding to variables in each figure with the Pearson correlation coefficient (r). (a) Spectral decay parameter values versus magnitudes. A red dashed line represents the regression line. (b) Lengths of frequency windows versus magnitudes. (c) Center frequencies of windows versus magnitudes. (d) Spectral decay parameters versus lengths of frequency windows. (e) Spectral decay parameters versus center frequencies of windows. (f) Center frequencies versus epicentral distances. The color version of this figure is available only in the electronic edition.

The relationships between κ ‐values, magnitudes, and variables related... Available to Purchase

Published: 11 February 2025
Figure 10. The relationships between κ ‐values, magnitudes, and variables related to frequency windows. The red dashed lines in each figure represent the regression lines corresponding to variables in each figure with the Pearson correlation coefficient ( r ). (a) Spectral decay parameter
Journal Article

High‐Frequency Spectral Decay Characteristics of Seismic Records of Inland Crustal Earthquakes in Japan: Evaluation of the f max and κ Models Available to Purchase

Masato Tsurugi, Reiji Tanaka, Takao Kagawa, Kojiro Irikura
Published: 10 March 2020
Bulletin of the Seismological Society of America (2020) 110 (2): 452–470.
DOI: https://doi.org/10.1785/0120180342
... model (commonly used in worldwide), the exponential spectral decay model, described by the parameter κ and the specific frequency f E at which a spectrum starts to decrease linearly with increasing frequency in log–linear space. For large earthquakes, we estimated f max to range from 6.5 to 9.9 Hz and s...
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View PDF for article title, High‐Frequency <span class="search-highlight">Spectral</span> <span class="search-highlight">Decay</span> Characteristics of Seismic Records of Inland Crustal Earthquakes in Japan: Evaluation of the f max and κ Models
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Journal Article

Importance of Considering Near‐Surface Attenuation in Earthquake Source Parameter Estimation: Insights from Kappa at a Dense Array in Oklahoma Available to Purchase

Hilary Chang, Rachel E. Abercrombie, Nori Nakata
Published: 03 January 2025
Bulletin of the Seismological Society of America (2025)
DOI: https://doi.org/10.1785/0120240137
...Figure 3. High‐frequency spectral decay parameter kappa ( κ ) measured from the vertical component of the acceleration spectra of regional event R1. (a)  P arrival for κ p , acc and (b)  S arrival for κ s , a c c . The spectra are stacked among stations within...
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View PDF for article title, Importance of Considering Near‐Surface Attenuation in Earthquake Source <span class="search-highlight">Parameter</span> Estimation: Insights from Kappa at a Dense Array in Oklahoma
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Journal Article

High‐Frequency Spectral Decay in P ‐Wave Acceleration Spectra and Source Parameters of Microearthquakes in Southeastern Sicily, Italy Available to Purchase

Giuseppina Tusa, Horst Langer, Alfonso Brancato, Stefano Gresta
Published: 01 August 2012
Bulletin of the Seismological Society of America (2012) 102 (4): 1796–1809.
DOI: https://doi.org/10.1785/0120110206
... contradictory results and suggest that there are still unresolved aspect on the origin of high‐frequency spectral decay. Investigations into the attenuation parameter κ of local earthquakes in southeastern Sicily were performed by Tusa and Gresta (2008) . The authors computed the parameter κ from...
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View PDF for article title, High‐Frequency <span class="search-highlight">Spectral</span> <span class="search-highlight">Decay</span> in P ‐Wave Acceleration Spectra and Source <span class="search-highlight">Parameters</span> of Microearthquakes in Southeastern Sicily, Italy
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Journal Article

Estimation of High‐Frequency Spectral Decay ( κ ) for the Gyeongju Area in South Korea Available to Purchase

Seon Jeong Park, Jung Mo Lee, Chang‐Eob Baag
Published: 17 December 2019
Bulletin of the Seismological Society of America (2020) 110 (1): 295–311.
DOI: https://doi.org/10.1785/0120180345
...Seon Jeong Park; Jung Mo Lee; Chang‐Eob Baag ABSTRACT The high‐frequency spectral decay parameter kappa ( κ ) is estimated for the Gyeongju area using records of the temporary seismic array in the Gyeongju area (TSAG), which operated from 2010 to 2013. Gyeongju is a city located in the southeastern...
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View PDF for article title, Estimation of High‐Frequency <span class="search-highlight">Spectral</span> <span class="search-highlight">Decay</span> ( κ ) for the Gyeongju Area in South Korea
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Journal Article

A Least Squares Method For Objective Determination of Earthquake Source Parameters Available to Purchase

John G. Anderson, James R. Humphrey, Jr.
Published: 01 July 1991
Seismological Research Letters (1991) 62 (3-4): 201–209.
DOI: https://doi.org/10.1785/gssrl.62.3-4.201
... parameters can be resolved for events with moment magnitudes in the range M W = 3 - M W = 6. For smaller events (M W = 1 - M W = 2), moment and spectral decay parameter are still well determined from low frequencies in the data. The average corner frequency is stil reasonable in this case...
View PDF for article title, A Least Squares Method For Objective Determination of Earthquake Source <span class="search-highlight">Parameters</span>
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Journal Article

Estimation of κ 0 Implied by the High‐Frequency Shape of the NGA‐West2 Ground‐Motion Prediction Equations Available to Purchase

Arash Zandieh, Kenneth W. Campbell, Shahram Pezeshk
Published: 24 May 2016
Bulletin of the Seismological Society of America (2016) 106 (3): 1342–1356.
DOI: https://doi.org/10.1785/0120150356
... of this figure is available only in the electronic edition. 20 March 2016 The attenuation of ground‐motion acceleration at high frequencies is often parameterized by the spectral‐decay parameter kappa ( κ ). Kappa was first introduced by Anderson and Hough (1984) to model the high...
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View PDF for article title, Estimation of κ 0 Implied by the High‐Frequency Shape of the NGA‐West2 Ground‐Motion Prediction Equations
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Journal Article

Shear-wave attenuation and site response in Guerrero, Mexico Available to Purchase

James R. Humphrey, Jr., John G. Anderson
Published: 01 August 1992
Bulletin of the Seismological Society of America (1992) 82 (4): 1622–1645.
DOI: https://doi.org/10.1785/BSSA0820041622
... source and an exponential decay term, e −πκ f , to describe the high-frequency spectral shape. The spectral decay variable, κ, associated with attenuation, is parameterized as the sum of a distance dependent component, κ ˜ ( r ) , and a site term, κ 0 ( S ), which takes a different value for each site, S...
View PDF for article title, Shear-wave attenuation and site response in Guerrero, Mexico
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Journal Article

Stochastic Finite‐Fault Modeling of Ground Motion for the 2010 Rigan Earthquake, Southeastern Iran Available to Purchase

Maryam Safarshahi, Mehdi Rezapour, Hosein Hamzehloo
Published: 01 February 2013
Bulletin of the Seismological Society of America (2013) 103 (1): 223–235.
DOI: https://doi.org/10.1785/0120120027
...Figure 6. Dependence of spectral decay parameter on epicentral distance ( R ) for longitudinal and transverse components. The color version of this figure is available only in the electronic edition. ...
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View PDF for article title, Stochastic Finite‐Fault Modeling of Ground Motion for the 2010 Rigan Earthquake, Southeastern Iran
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An empirical study of earthquake source spectra for California earthquakes Available to Purchase

Gail M. Atkinson, Walt Silva
Published: 01 February 1997
Bulletin of the Seismological Society of America (1997) 87 (1): 97–113.
DOI: https://doi.org/10.1785/BSSA0870010097
... of subfaults, each of which is represented by a Brune omegasquared point source, correctly matches the observed spectral shapes and amplitudes. The spectral decay parameter kappa, representing average near-surface attenuation of high-frequency motion at rock sites, increases with increasing magnitude, from...
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